details

property	value
status	complete
benchmark	#4.22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.018715 seconds
cpu usage	0.019221
user time	0.007365
system time	0.011856
max virtual memory	113188.0
max residence set size	4300.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,s(z:S),s(z:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,s(z:S),s(z:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,s(z:S),s(z:S)) -> Rules: quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,s(z:S),s(z:S))) Problem 1: SCC Processor: -> Pairs: QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,s(z:S),s(z:S)) -> Rules: quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,s(z:S),s(z:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,s(z:S),s(z:S)) ->->-> Rules: quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,s(z:S),s(z:S))) Problem 1: Subterm Processor: -> Pairs: QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,s(z:S),s(z:S)) -> Rules: quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,s(z:S),s(z:S))) ->Projection: pi(QUOT) = 1 Problem 1: SCC Processor: -> Pairs: QUOT(x:S,0,s(z:S)) -> QUOT(x:S,s(z:S),s(z:S)) -> Rules: quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,s(z:S),s(z:S))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. popout

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